This application is a Continuation Application of PCT Application PCT/JP2004/011598, filed on Aug. 12, 2004, the contents of which are herein wholly incorporated by reference. This invention relates to a method and apparatus for directions-of-arrival (DOAs) estimation of radio waves impinge on an array antenna at a base station and relates to an apparatus of base station that variably controls the beam directivity of the antenna based on the estimated directions of radio waves (also be referred to as signals from the aspect of signal processing hereafter). Further, this invention relates to a method and apparatus for estimating the directions of multiple incoming signals (mutually uncorrelated signals, or partially correlated signals, or fully correlated (i.e., coherent) signals) in an on-line manner and quickly tracking the time-varying directions.
In recent years, research and development on applications of adaptive array antenna for mobile communications have attracted much attention. Herein an antenna created by placing multiple antenna elements at different spatial positions with a certain geometric shape is called an array antenna. The problem of estimating the directions of radio waves impinging on the antenna is one of the important fundamental techniques of an adaptive array antenna. For the problem of estimating the direction of a signal, subspace-based methods that use the orthogonality between the signal subspace and noise subspace are well known because of their good estimation accuracy and low computational load. A typical example is the MUSIC (multiple signal classification) (see non-patent document 1: R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antenna Propagation, vol. 34, no. 3, pp. 276-280 (1986). Also for the problem of direction estimation of coherent signals, the subspace-based method with preprocessing is well known as the spatial smoothing based MUSIC (see non-patent document 2: J. Shan, M N. Wax and T. Kailath, “On spatial smoothing for arrival direction estimation of coherent signals,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 4, pp. 806-811 (1985); and non-patent document 3: S. U. Pillai and B. H. Kwon, “Forward/backward spatial smoothing techniques for coherent signals identification,” IEEE Trans. Acoust., Speech, Signal, vol. 37, no. 1, pp. 8-15 (1989)).
In conventional subspace-based methods, in order to obtain the signal (or noise) subspace, it is necessary to perform eigendecomposition processing such as eigenvalue decomposition (EVD) or singular value decomposition (SVD) on the array covariance matrix. Also, in practical mobile communication systems, the signals from a user (i.e, mobile terminal) that are usually reflected from buildings or the like and impinge on the array antenna at base station via a direct path and some reflected paths, hence the direction estimation in a multipath propagation environment is very important. Furthermore, the directions of incident signals may change over time due to the movement of user (i.e., signal source), thus a tracking method is required to estimate the directions in an on-line manner.
However, when conventional subspace-based methods are used to estimate the time-varying directions in real-time, it is necessary to perform the EVD (or SVD) repeatedly, and hence the computational loads of these methods become very heavy and much processing time is required.
In order to explain the disadvantages of the conventional subspace-based DOA estimation methods, the spatial smoothing based MUSIC proposed in non-patent document 2 will be briefly described.
Here, it is assumed that p narrowband signals {sk(n)} are incident on a uniform linear array (ULA) with M elements from angles {θk}. The signals received at the array elements can be expressed by the following equation 1.
                              y          ⁡                      (            n            )                          =                ⁢                                            [                                                                    y                    1                                    ⁡                                      (                    n                    )                                                  ,                                                      y                    2                                    ⁡                                      (                    n                    )                                                  ,                …                ⁢                                                                  ,                                                      y                    M                                    ⁡                                      (                    n                    )                                                              ]                        T                    =                                                    A                ⁡                                  (                                      θ                    ⁡                                          (                      n                      )                                                        )                                            ⁢                              s                ⁡                                  (                  n                  )                                                      +                          w              ⁡                              (                n                )                                                                        (        1        )                                          A          ⁡                      (                          θ              ⁡                              (                n                )                                      )                          ⁢                  =          Δ                ⁢                ⁢                  [                                    a              ⁡                              (                                                      θ                    1                                    ⁡                                      (                    n                    )                                                  )                                      ,                          a              ⁡                              (                                                      θ                    2                                    ⁡                                      (                    n                    )                                                  )                                      ,            …            ⁢                                                  ,                          a              ⁡                              (                                                      θ                    p                                    ⁡                                      (                    n                    )                                                  )                                              ]                                                                              a          ⁡                      (                                          θ                k                            ⁡                              (                n                )                                      )                          ⁢                  =          Δ                ⁢                ⁢                              [                          1              ,                              ⅇ                                  j                  ⁢                                                                          ⁢                                      w                    o                                    ⁢                                      τ                    ⁡                                          (                                                                        θ                          k                                                ⁡                                                  (                          n                          )                                                                    )                                                                                  ,              …              ⁢                                                          ,                              ⅇ                                  j                  ⁢                                                                          ⁢                                                            w                      o                                        ⁡                                          (                                              M                        =                        1                                            )                                                        ⁢                                      τ                    ⁡                                          (                                                                        θ                          k                                                ⁡                                                  (                          n                          )                                                                    )                                                                                            ]                    T                                                                                          s            ⁡                          (              n              )                                =                    ⁢                                    [                                                                    s                    1                                    ⁡                                      (                    n                    )                                                  ,                                                      s                    2                                    ⁡                                      (                    n                    )                                                  ,                …                ⁢                                                                  ,                                                      s                    p                                    ⁡                                      (                    n                    )                                                              ]                        T                          ,                                                                      w          ⁡                      (            n            )                          =                ⁢                              [                                                            w                  1                                ⁡                                  (                  n                  )                                            ,                                                w                  2                                ⁡                                  (                  n                  )                                            ,              …              ⁢                                                          ,                                                w                  M                                ⁡                                  (                  n                  )                                                      ]                    T                                                                                          w            0                    =                    ⁢                      2            ⁢            π            ⁢                                                  ⁢                          f              0                                      ,                              τ            ⁡                          (                                                θ                  k                                ⁡                                  (                  n                  )                                            )                                ⁢                      =            Δ                    ⁢                                    (                              d                /                c                            )                        ⁢            sin            ⁢                                                  ⁢                                          θ                k                            ⁡                              (                n                )                                                                                    where f0, c and d are the carrier frequency, propagation speed, and element interval (half wavelength of the carrier wave), respectively, (·)T denotes the transposition, a(θk(n)) and A(θ(n)) are the array response vector and response matrix, and w1(n) is the temporally and spatially uncorrelated white Gaussian noise with zero-mean and variance σ2.
First, the case of estimating constant directions will be considered, i.e., θk(n)=θk. For simplicity, A(θ(n)) will be expressed as A below. Here, the array covariance matrix is expressed by the following equation.
                    R        ⁢                  =          Δ                ⁢                              E            ⁢                          {                                                y                  ⁡                                      (                    n                    )                                                  ⁢                                                      y                    H                                    ⁡                                      (                    n                    )                                                              }                                =                                                    AR                s                            ⁢                              A                H                                      +                                          σ                2                            ⁢                              I                M                                                                        (        2        )            
where E(·) and (·)H express the expectation and the complex conjugate transposition respectively, and Rs=E[s(n)sH(n)] is the source signal covariance matrix, and IM is an M×M identity matrix. Furthermore, the correlation rik between the received data yi(n) and yk(n) is defined by rik=E{yi(n)y*k(n)], where rik=r*ki, exists, and (·)* expresses the complex conjugate. Also, the array covariance matrix R of equation (2) can be clearly expressed by the following equation.
                    R        =                  [                                                                      r                  11                                                                              r                  12                                                            …                                                              r                                      1                    ⁢                    M                                                                                                                        r                  21                                                                              r                  22                                                            …                                                              r                                      2                    ⁢                    M                                                                                                      ⋮                                            ⋮                                            ⋰                                            ⋮                                                                                      r                                      M                    ⁢                                                                                  ⁢                    1                                                                                                r                                      M                    ⁢                                                                                  ⁢                    2                                                                              …                                                              r                                      M                    ⁢                                                                                  ⁢                    M                                                                                ]                                    (        3        )            
In the spatial smoothing based MUSIC for estimating the directions {θk} of coherent signals, the entire array is divided into L overlapped subarrays with m (1≦m≦M) elements as shown in FIG. 1. Here, m and L are called the subarray size and the number of subarrays, where L=M−m+1. From Equation 1, the signal vector of the 1 th subarray y1(n) can be expressed by Equation 4.y(n)=[y1(n),yl+1(n), . . . , y1+M−1(n)]T=AmDI−1s(n)+w1(n)Am=[am(θ1),am(θ2), . . . , am(θp)]am(θk)=[1,ejwoτ(θk), . . . , ejwo(m=1)τ(θis k)]T w(n)=[w1(n),wI+1(n), . . . , wI−m+1(n)]T  (4)for 1=1, 2, . . . , L, where D is a diagonal matrix with elements ejw0τ(θ1), ejw0τ(θ2), . . . , ejw0τ(m−1)τ.(θp), and am(θk) and Am are the subarray response vector and response matrix. The 1 th subarray covariance matrix is given by Equation 5.R1=E{yI(n)yIH(n)}=AmDl−1Rs(Dl−1)HAmH+σ2Im  (5)Then by spatially averaging the L subarray covariance matrices {R1}, a covariance matrix is obtained as Equation 6.
                              R          _                =                              1            L                    ⁢                                    ∑                              l                =                1                            L                        ⁢                          R              l                                                          (        6        )            Hence the EVD of this spatially averaged covariance matrix is given by Equation 7 below.
                              R          _                =                                            ∑                              i                =                1                            m                        ⁢                                          λ                i                            ⁢                              e                i                            ⁢                              e                i                H                                              =                      E            ⁢                                                  ⁢            Λ            ⁢                                                  ⁢                          E              H                                                          (        7        )            Here, ei and λi are the eigenvectors and eigenvalues of the matrix R, E is a matrix having a column {ei} and A is a diagonal matrix having elements {λ1}. Also, the spaces spanned by the signal vectors {e1, e2, . . . ep} and noise vectors {ep+1, ep+2, . . . em} are called the signal subspace and noise subspace, respectively. Further the signal subspace can be expressed by using the array response vector. The direction estimation method based on the orthogonal relationship between the signal subspace and the noise subspace is called subspace-based method.
By using eigenvalue analysis of the covariance matrix R of Equation 7, the following orthogonal relationship is established between the noise vectors {ep+1, ep+2, . . . em} and the subarray response vector am(θk) that belongs to the signal subspace.eiHam(θk)=0  (8)for i=p+1, p+2, . . . m. From this orthogonal relationship, it is possible to calculate a spectrum as given by the equation below.
                                                        P              _                        ssmusic                    ⁡                      (            θ            )                          =                  1                                    ∑                              i                =                                  p                  +                  1                                            m                        ⁢                                                                                                e                    i                    H                                    ⁢                                                            a                      m                                        ⁡                                          (                      θ                      )                                                                                                  2                                                          (        9        )            where am(θ)=[1,ejw0τ(θ), ejw0(m−1)τ(θ)]T. Then the spatial smoothing based MUSIC estimates the directions of multiple incoming waves from the positions of p highest peaks of the spectrum given by Equation 9.
As shown in Equation 7, in subspace-based estimation methods such as the spatial smoothing based MUSIC, it is necessary to perform the EVD of the array/subarray covariance matrix in order to obtain the signal or noise subspace. However, in actual array implementations, particularly when the number of array elements is large or when the time-varying directions should be estimated in an on-line manner, the EVD (or SVD) process becomes computationally intensive and time-consuming. Therefore, applications of conventional subspace-based methods with eigendecomposition (i.e., EVD or SVD) are limited by the computational load thereof. Therefore, when the directions of the incident waves change over time, it is not possible to estimate these DOAs quickly and with high accuracy by using conventional methods, and it becomes impossible to generate an accurate receiving/transmitting beam at the base station, correspondingly the performance of the receiving and transmitting system of the base station will degrade.
Recently, some methods for adaptive direction estimation and tracking that do not use eigendecomposition have been proposed, for example, the adaptive SWEDE method (subspace-based methods without Eigendecomposition) (non-patent document 4: A. Eriksson, P. Stoica, and T. Soderstrom, “On-line subspace algorithms for tracking moving sources,” IEEE Trans. Signal Processing, vol. 42, no. 9, pp. 2319-2330 (1994)). However, in the case of coherent signals, low signal-to-noise ratio (SNR) or small number of data, the performance of these methods becomes poor, and the amount of computational load required by these methods that use Least squares (LS) is large.
Moreover, the inventor has proposed a method and apparatus for estimating and tracking the direction of radio waves based on the cyclostationarity of communication signals (refer to non-patent document 5: J. Xin and A. Sano, “Directions-of-arrival tracking of coherent cyclostationary signals in array processing,” IEIC Trans. Fundamentals vol. E86-A, no. 8, pp. 2037-2046 (2003), or patent document 1: International patent application PCT/JP03/08015; U.S. Pat. No. 7,084,812). But this method uses the temporal property the cyclostationary signals.
Furthermore, the inventor has proposed a computationally efficient direction estimation method called SUMWE (subspace-based method without eigendecomposition) (refer to non-patent document 6: J. Xin and A. Sano, “Computationally efficient subspace-based method for arrival direction estimation with eigendecomposition,” IEEE Trans. Signal Processing, vol. 52, no. 4, pp. 876-893 (2004), or patent document 2: International patent application PCT/JP03/06411; U.S. Pat. No. 7,068,211). However, the online DOA estimation and the tracking of time-varying directions are not considered in this method.